# Properties

 Label 4592.l Number of curves $2$ Conductor $4592$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 4592.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4592.l1 4592f2 [0, 0, 0, -153781003, 734010288314] [] 592704
4592.l2 4592f1 [0, 0, 0, -309643, -61048006] [] 84672 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4592.l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4592.l do not have complex multiplication.

## Modular form4592.2.a.l

sage: E.q_eigenform(10)

$$q + 3q^{3} - q^{5} - q^{7} + 6q^{9} + 2q^{11} - 3q^{15} - 3q^{17} + 8q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.